Against a backdrop of a worsening global warming problem and an energy problem, demands for an automobile to improve fuel efficiency and reduce a CO2 emission amount have been increasing higher than ever before. An idle stop is effective for improving the fuel efficiency and reducing the CO2 emission amount. However, there is a problem that exhaust (mainly, NOx) is deteriorated at the restart after the idle stop. This is caused by an oxygen storage/release function with which a catalyst is generally provided and which is referred to as an OSC (O2 Storage Capacity). The OSC function serves as a function of storing oxygen in a lean atmosphere (oxidizing atmosphere) with respect to a stoichiometric state, and conversely, serves as a function of releasing oxygen in a rich atmosphere (reducing atmosphere) with respect to the stoichiometric state. For this reason, when fuel injection is stopped during the idle stop, air (having a high oxygen concentration) flows out into an exhaust pipe, and hence the inside of the catalyst is brought into an oxygen saturation state (strong oxidizing atmosphere) by the OSC function. If an engine is restarted in this state, a gas emitted from the engine is stoichiometric or rich, and hence oxygen is released due to the OSC function. As a result, the atmosphere inside of the catalyst changes from the strong oxidizing atmosphere to the stoichiometric atmosphere. However, the atmosphere inside of the catalyst is the oxidizing atmosphere during a given period which is the transition period therefor, and hence HC and CO are purified (oxidized), whereas NOx cannot be purified (reduced).
For example, Patent Document 1 given below discloses a method in which, if an oxygen sensor downstream of a catalyst detects a lean state at the restart after an idle stop, it is determined that the atmosphere inside of the catalyst is lean, whereby rich control is performed.    Patent Document 1: JP Patent Publication (Kokai) No. 2006-37964 A